CALCULUS Er REVIJ

-. Fmdthefouow4flglimits.

LAm 4x2Lima) 2”’ x—,O 5x3—3x’

tim 4_3tim x2+3x—18x—3 —3b)

x—,3 —9

lAm 7x2—5x h)C) urn—3x+9x2 x--

)irn (x—1)2 * 4x3 X3

Jimd) 2’

X-+t [Th+Z)2+ 5 - 3

LAm x’+125 k) urn 1-3n-2n2

_________

t-— 3n25n—6e)x——5 x1—2x—3$

2 _a, ifx<12. t f(x= { (x-1)3 1, ii x1

Find the following limits, if they exist.

a) urn f(x) b) urn f(x) c) urn f(x)x-

3 Find the derivative of y = ‘/I using the limit process.

q Findtheequationofthetangentstoyx3+3x2—5x+9paralleltoy=4x+9.

Differentiate the following fuctions. Dc..fl9I simplify your answers.

a) y=(7x1—3x2)’ f(x) — (3x2—1>4(5x—2)

b) ‘i= (x+3)2+(5x—1)* ( x+

kxa+3x)

c) y(7x5—3)(8x4+7)

9x7 — 3xd) y=5x3 + 7x2

e) y = (5x1 — 3x)g(9x — 7)1

f) y=4(5d_3)4_(7x+52

Given the following graph of y=f(x):

a) At what x value(s) is the function discontinuous?b) At what x value(s) is the function not differentiable?c) List all the critical points.d) At what interval(s) is the graph increasing?e) What is the absolute maximum value?f) What is the absolute minimum value?

4. If y’ = (2x — 3)(x + lX4x +7), find the intervals for which y. is Increasing.

r1, Given f(x) — — 8x3 + 18x2 — 15

a) find each of the following:

i) all critical points off;ii) the interval(s) where f is increasing;iii) the interval(s) where f is decreasing;iv) all local maximum and local minimum values.

b) Using the information obtained in a), sketch the graph of f(x) (labelcompletely).

?. Given the function f (x) 2x - X, fmd the equations of the horizontalx2-3x-4

and vertical asymptotes.

Sketch the curve by discussing the relation under the headings

a> domain

b) intcrceprs

c) asymptotesmaximum andjor minimum points.

>1

;4—

.1::

r

Y

&)

<?

‘T

r

+r—

;>

\

c’J

-b

j:r

c

r

6N

tç

I)C

)

/‘l’

)Gc

)L

J(

-

$4

I

I

r’4v

1)p

Il‘1

+,

1*

4”

(0

$,

•4’

•‘

N

l7

’;‘i’

c__

1L—;,

t_b

li

I-

.4-

r”

1

04,

1>

Q

ct’

3

I(lj

e

‘I .3..

I,

Iv

A

I

(*tI})t1/

I4-I-

(LAL±2J1)•1

(2A)/

LI

j,

,

-,

-4-(3.

_

.4.-.

)(‘)\S

-.4.-

*

0-

$(1

-f

-

s__sZD

--..-.V

II)

ci-

—

_j_

_;.-—

(1(I

c—o

z:.

-c‘—

s—

—:i

—Zl

—4

>c> 4

‘I

c1J

Cj

) ‘s1 >,

4-

-U

LIIC -

—ca

—zr

c—’

ci4 4

—-

C-)

N

p..

L

4 -:1

.4-1- :E

j‘a

+

——

4

0

-

-C.

iE4 >

Is

5—

5-—

5-—

—0

‘CT

h

4 1

I’

4Is

)

+

11-

Cv i

(—5-’

5--

>>

‘=

i\

><

>ç)

fl

AJ

iJ

I)

clc

FL

c)

L’)

V

Ij

If(I

I’ (J

U

(I

(rjoc\

>i

I

I L)

--

-p

z— ?t tI

Qj6&3s

co Discicc. frcwej(J duny f1$ s’c

f(s) 9c(}/

z (0 -I ÷ / 7- fr)f J ZS —-(

(p32

c)

7-L

7)

I()

‘44

l1

}

j- ‘cV

0 (-sj(-

-Qz tf8 /

C)

I

é: 3

‘yc-

5’

()/4j

z______*

—/2

jA)5f/7

(o)h—

/—

+II(c)

F71c

Is4_9

(-)(I)20

0

(,

40

()s3(9

IA

-A

1H41

I)

+

‘I0f)

I

LI

—

‘IP—si—

-Il

ccs1

(JJl

‘1‘1

E1

c1

(t1fc

l4AfjILC‘

—

;PjjJPwvvv\ 4v

4((Jj‘-I

Ih

cot‘I

cc,

V’ 0

eut1If

J

‘i:rv

I

QpI

4jt1L)-A

9’

‘h1

‘49,

0

X)(14(

-

1UJt?(irX)

fr—xL)

o‘)‘y

(1ih)

\-

-1--4-

3<)cX?)_

17(

MrlvIWPcrrv?7rfJ.

7)‘(s2}’(b

(ti’D)Io:4 9(

ti)‘O)rv

fr

6J

(‘SI_‘0,)

9JVw/r1ryøvt(si-j

(cs’)L1

[to

4

*

—I-

-f:;;)c70

—Ij’q

÷It1I_)I

‘cii

(h,_)C)h

H-2- -U

h

(o

Y1V

J

(1()(sio)9Vr

(ci

(o

0U

I

II

0f

I,

I,

+h

}

-d

II1

lj

-r—

4

4I

$0’

()

‘()

1

----4

-

_i_,

\_

__

)‘_

)

)[D

?iI çv

I-

r4Di

I

___

(.)

ml4

H

Ia,

-.4

C

I

c